The problem has a nicer answer if it is actually
x^(3/2) = 27
You solve this by raising both sides to the 2/3 power
(x^(3/2))^(2/3) = 27^(2/3)
x^((2/3)*(2/3)) = ((27^(1/3))^2
x = 3^2
x = 9
You can also solve it using logarithms.
(3/2)Log[x] = Log[27]
Log[x] = (2/3)Log[27] ≈ (2/3)*1.43136 ≈ .95424
x = 9
If your original problem is the one you want, then the answer is found by multiplying by 2 and taking the cube root.
X^3/2 = 27
x^3 = 27*2
x = 27^(1/3)*2^(1/3)
x = 3*2^(1/3) ≈ 3*1.25992 ≈ 3.77976
x^(3/2) = 27
You solve this by raising both sides to the 2/3 power
(x^(3/2))^(2/3) = 27^(2/3)
x^((2/3)*(2/3)) = ((27^(1/3))^2
x = 3^2
x = 9
You can also solve it using logarithms.
(3/2)Log[x] = Log[27]
Log[x] = (2/3)Log[27] ≈ (2/3)*1.43136 ≈ .95424
x = 9
If your original problem is the one you want, then the answer is found by multiplying by 2 and taking the cube root.
X^3/2 = 27
x^3 = 27*2
x = 27^(1/3)*2^(1/3)
x = 3*2^(1/3) ≈ 3*1.25992 ≈ 3.77976